Problem:
A subset of the set of integers from to , inclusive, has the property that no two elements of sum to . What is the maximum possible number of elements in
Answer Choices:
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Solution:
Several pairs of numbers from to sum to . These pairs are , . Set can have at most one number from each of these pairs. In addition, can contain all of the numbers since these cannot be paired with any of the available numbers to sum to . So has at most numbers. The set containing the first positive integers, for example, is one of these maximum sets.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions